Change: First Order Logic

created on March 1, 2013, 7:45 p.m. by Hevok & updated on March 1, 2013, 7:45 p.m. by Hevok

First Order Logic (FOL) is very powerful. In First Order Logic one has Quantifiers. Quantifiers, or Quantors, allow Assertion of Sets of Objects even without naming these Objects explicitly.

So one can make Statements like All Humans are mortal and than one can pick out one Human and say it is a Human and because one previously stated that all Humans are mortal it can be deduced that Hevok must be moral too. Thus, one can make Deductions out of these Sentences/Statements. Normally one has a general Statement, then a special Statements and then one can infer implicit knowledge that is given in the Generalization. FOL is perfectly suited for a Description of Ontologies, but it is rather expressive, which means it is much more too expressive. On the other hand it is also very complex when it comes to Computation. It is not only complex some of the Calculations in Logical Calculus for First Order Logic are not decidable, i.e. not computable.

Overall the expressiveness of the First order Logic means for Models it is rather Bulky. It is also very Bulky because one can express the same the Subject, the Knowledge in various different Forms and therefore one has the problem to find a unique Form or unique Representation for the Knowledge. Thus, it is difficult to achieve Consensus about a Model. Another issue is that it is rather complex to Proof if one wants to proof the Correctness or Completeness of Assertions.

One needs to look at some better suited Fragments of First Order Logic. Something that lies between Propositional Logic and First Order Logic. It need to be something that is almost as expressive as First Order Logic but does not have its Disadvantages like for example the complexity or the expressiveness as well as the ambiguity.

• In the First Order Logic (FOL) Quantors allow Assertions about Sets of Objects, without naming the Objects explicitly.

  All Humans are mortal. Hevok is a Human. Hevok is mortal.

• FOL is perfectly suited for the Description of Ontologies, but ..

  • FOL is rather expressive,
  • therefore also rather bulky for Modeling,
  • difficult to achieve consensus in Modeling and
  • rather complex to Proof (Correctness and Completeness of Assertions)
• Therefore: look for some well suited Fragment of FOL!

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